{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "data = np.loadtxt('data100m.csv',delimiter=',')\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "x = data[:,0][:,None]\n",
    "t = data[:,1][:,None]\n",
    "x = x - x[0]\n",
    "x = x/4.0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_w():\n",
    "    muw = np.array([[ 11.12293727], [ -0.05319782]])\n",
    "    siw = np.array([[ 0.28106107, -0.01545975], [-0.01545975 , 0.00118833]])\n",
    "    w_samp = np.random.multivariate_normal(muw.flatten(),siw,1)\n",
    "    return w_samp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1094b7110>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HD6fgmNILAwZ0Tiqf201h3rKFQr17Nx+bjA9j+5iG2UTTKSkU6sxMnuvQofyM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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10949bf10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x,t,'ro')\n",
    "\n",
    "pred35 = []\n",
    "pred50 = []\n",
    "\n",
    "for i in range(1000):\n",
    "    w = generate_w()\n",
    "    plt.plot((x[0],x[-1]),(w[0][0]+w[0][1]*x[0],w[0][0]+w[0][1]*x[-1]),'b')\n",
    "    pred35.append(w[0][0] + w[0][1]*35)\n",
    "    pred50.append(w[0][0] + w[0][1]*50)\n",
    "    \n",
    "plt.plot(x,t,'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   2.,   12.,   46.,  130.,  221.,  257.,  186.,  109.,   30.,    7.]),\n",
       " array([  6.40415396,   6.93980558,   7.4754572 ,   8.01110882,\n",
       "          8.54676044,   9.08241205,   9.61806367,  10.15371529,\n",
       "         10.68936691,  11.22501853,  11.76067015]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2e6290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pred35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   3.,   12.,   55.,  118.,  220.,  270.,  183.,  100.,   29.,   10.]),\n",
       " array([  3.95141469,   4.80019598,   5.64897728,   6.49775857,\n",
       "          7.34653986,   8.19532115,   9.04410245,   9.89288374,\n",
       "         10.74166503,  11.59044633,  12.43922762]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tk5Tk1CRfSLI7ybeTvHnSNU1Kko8k+VaSh5PckuSkSdc0LkluSjKX5OF5bWuTbE/yaJJ7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b352890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pred50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
